We study statistical models that are parametrized by squares of linear forms. All critical points of the likelihood function are real and positive. There is one critical point in each region of the projective hyperplane arrangement defined by the linear forms. We examine the ideal and singular locus of the model, and we give a determinantal presentation for its likelihood correspondence. We characterize tropical degenerations of the MLE, we describe the log-normal polytopes, and we explore connections to determinantal point processes.

翻译：我们研究由线性形式的平方参数化的统计模型。似然函数的所有临界点均为实数且为正。在由线性形式定义的射影超平面排列的每个区域中，存在一个临界点。我们考察了模型的理想与奇异轨迹，并给出了其似然对应的行列式表示。我们刻画了最大似然估计的热带退化，描述了对数正态多面体，并探讨了与行列式点过程的联系。